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Emerson’s First Part. 


2. 
THE 


NORTH AMERICAN 


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4 


AR ITOH M EEL e: 


PART FIRST, 


FOR 


YOUNG LEARNERS. 


BY FREDERICK EMERSON, 


LATE PRINCIPAL IN THE DEPARTMENT OF SN 
BOYLSTON SCHOOL, BOSTON. 


CLAREMONT: 
CLAREMONT MANUFACTURING COMPANY. 


i 


1844, 


nae 8s 


ALIAS A PAAPL PEAS FADES DESLIS SSOP SAAS AL SPSS SATO 
Entered accordingeto Act of Congress, in the year 1838, by Frederick Emerson, 
in the Clerk?s Office of the District Court of the District of Massachusetts. 


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PREFACE. 


In a systematic course of general education, Arithmetic claims 
a place among the primary objects. Its elementary exercises, 
when rationally conducted, are adapted to the capacities of 
children at a very early age. Its influence on the character of 
children, in developing the reasoning faculties, and habituating 
the mind to investigation, is highly conducive to progress in every 
other branch of knowledge. Notwithstanding the obvious truth 
of this remark, the practice of postponing arithmetic till children 
arrive at the age of nine or ten years, still prevails in many of 
our schools, and calls for the attention of those whose influence 
may correct the error. 

The purpose of this manual is, to facilitate the instruction of 
the younger elasses, It contains the ‘first part of a Course of 
Evercises in Arithmetic, which is published in three books, 
severally denominated, Parr First, Parr Srconp, and Parr 
Turrp. The method employed for illustrating the subject, it 
will be seen, is original and peculiar. 

Parr Fins‘ is confined to the simple elements, and it may be 
advantageously used as an introduction to the subsequent study 


_of arithmetic from any larger book now in common use. Learn- 


ers will, however, find the steps of progress to be most gradual, 
easy, and certain, in passing from this book immediately into 
Part Second. 

The lessons contained in Part First are all to be performed 
orally ; the slate and pencil not being required. In the title-page 
will be seen a drawing of an improved structure of the Abacus. 
It is a convenient apparatus for illustrating the combinations of 
numbers ; although it need not be used in teaching from this 
dook: its use is superseded by cuts and unit marks. 4 

| Oe 


Boston, August 1, 1838. 


{> This book is adopted in the Public Schools of the cities 
of Boston, Salem, Portland, Providence, New York, Philadelphia, 
and Louisville, by orders of the respective Boards of School 
Committee and Trustees. 


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ARI PHMETIC. 
NUME RATION. 
Note to Teachers. The learners are to have their hooks open before 
them, while performing the lessons in Numeration. Do not omit auy lesson. 
ne 
Lesson First. I, ig 
Here is the picture of some apples:— count them 
On», two, three, four, five, Six, seven, eight, nine, ten, 


Oo0000 


See this flock of black-birds: they have lighted 
upon the bars of a gate, and are all singing toether, 
Find how iy there are on each separate bar. 


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4 NUMERATION. 


Lesson Seconp. II. 


Note to Teachers. Yn this lesson, the teacher may read the questions, and 
the children give the answers ; or, if the children can read with tluency, they 
may read the questions to each other, by turns; each one reading a question 
to be answered by the scholar next below him, and thus proceeding through 
the class. ‘his lesson should pass through the class several times at one 
recitation, until each scholar bas had several tarns in answering. ‘The chief 
~urpose of the lesson is to show, that numbers are formed, successively, by 
adding one unit to the next preceding number. 


How many stars are one star and one star? 


4 J 
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How many stars are two stars and one star? 


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How many stars are three starsand one star? 


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How many stars are four stars and. one star? 


Se we De We Me 
“7K Pe ten ee 2 


How many stars are five stars-and one star? 


Se We Ye IE SL we 
Anema: 2 IN PSP AN 71 


How many stars are six stars and one star? 
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2a Eee Y Pos 28) DRE. Sea Me ay 
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“How many stars are seven stars and one star i 


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“7X sat A os set 2} 7N GON PR ERR a 


How many stars are eight stars and one star? 


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How many stars are nine stars and one star? 


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NUMERATION. 5 


Lesson 'T'urrp. ILI. 


Note to Teachers. ‘Tne design of the preceding lessons has been, to teach 
the wames, and the comparative magnitude of numbers, from one to ten. 
The teacher should now imform the Jearners, that numbers are represented 
by FIGURES. He may direct them, to obtain the names of the figures by 
counting the unit marks, (from left to right,) which stand against the figures 
severally, in the following table. As this exercise will fend to fix a mental 
association of each figure with the number of units, which it represents, the 
lesson should not be omitted, even by children, who are already able to 
read figures. 


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NUMERATION. 


Lesson Fourtu. 


Note to Teachers. 


dren read the words in the columns. 
a slip of paper, and the reading be performed on the figures, 


IV. 


Make two exercises of this lesson. 
Then, let the words be covered with 


First, let the chil- 


While read- 


ing the figures, lead the children to observe the analogies, two — twentg ; 
three thirty; four — forty ; five—fifty; &c. 


OMe awh Wwe 


13 


One, 
two, 
three, 
four, 
five, 
SIX, 
seven, 
eight, 
nine, 
ten, 
eleven, 
twelve, 
thirteen, 


14 fourteen, 


fifteen, 
sixteen, 
seventeen, 


eighteen, 


nineteen, 
twenty, 
twenty-one, 
twenty-two, 
twenty-three, 
twenty-four, 
twenty-five, 
twenty-six, 
twenty-seven, 
twenty-eight, 
twenty-nine, 
thirty, 
thirty-one, 
thirty-two, 
thirty-three, 


34 
39 
36 
37 
38 
39 
40 
4] 
42 
43 
44 
45 
46 
47 
48 
49 
50 
ol 
52 
D3 
o4 


thirty-four, 
thirty-five, 
thirty-six, 
thirty-seven, 
thirty-eight, 
thirty-nine, 
forty, 
forty-one, 
forty-two, 
forty-three, 
forty-four, 
forty-five, 
forty-six, 
forty-seven, 
forty-eight, 
forty-nine, 
filiy, 
fifty-one, 
fifty-two, 
fifty-three, 
fifty-four, 
fifty-five, 
fifty-six, 
fifty-seven, 
fifty-eight, 
fifty-nine, 
Sixty, 
sixty-one, 
sixty-two, 
sixty-three, 
sixty-four, 
sixty-five, 
sixty-six, 


67 
68 
69 
70 
71 
T2 
73 
74 
T5 
76 
77 
73 
79 


80 


81 
82 
Be 

84 
85 
86 
87 
88 
89 


sixty-seven, 
sixty-eigh 5 
sixty-nine, 
seventy, 
seventy-one, 
seventy-two, 
seventy-three, 
séventy-four, 
seventy-five, 
seventy-six, 
seventy-seven, 
seventy-eight, 
seventy-nime, 
eighty, 
eighty-one, 
eighty-two, 
eighty-three, 
eighty-four, 
eighty-five, 
eighty-six, 
eighty-seven, 
eighty-eight, 
eighty-nine, 
nibety, 
ninety-one, 
ninety-two, 
ninety-three, 
ninety-four, 
ninety-five, 
ninety-six, 
ninety-seven, 
ninety-cight, 
ninety-nine, 
one hundred 


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NUMERATION. 


Lesson Firru. 


My, 


~ How many balls are there in the upper line, 


How 


any in the first and second lines, counted together ? 


ae. counted across the page from left to mght? 


How many in three lines? 
How many in five lines? 


How many in four lines? 
How many in six lines? 


How many in seven lines? 


lines? 


ten lines? 


45 


14 


Lesson SixTuH. 
Tell the numbers expressed by these figures. 


70. 
49 
82 
43 
16 
17 
50 
83 


38 
18 
ol 
84 
39 
72 
19 
oz 


How many in nine lines? 


How many in eight 


How many in 


VI. 


22 
59 
88 
23 
56 
24 
a7 


90 


11 
44 
25 
91 
T7 
26 
D9 
33 


92 
66 
27 
60 
93 
32 
65 


94 


“R ADDITION. 


ADDITION. 
Note to Teachers. Learners sould henceforth recite with closed books 


Very young children, however, may go through once with their books oper 
The table at the end of each lesson is to be committed to memory. 


Lesson First. f * « 
Tell me how many trees are 1 tree and Meck 


1 and 2 are how many : y? 


Henry’s sister gave him 1 apple, and his mother 
gave him 3 more. How many apples had Henry? 


land 3 are how many? 


James found 1 pear under the tree, and John gave 
‘him 4 more. How many pears had James then? | A 4 


l and 4 are how many ? 


Sarah’ s brother gave her 1 cherry, and her mother 
gave her 7 more. How aaa had Sarah then ? 


Tl and 7 are Here many ? 


Recite the table that begins, One and one are two. 


land 1 are 2 land 6-are 7 
land 2 are 3 land 7 are 8 
l and 8 are 4 land 8 are 9 
l and 4 are 5 land 9 are 10 
1 ane: 5 aré- 6 l and 10 are 11 
- a siti: m ers gD oF 


ADDITION. 9 


Lesson Seconp. Il. 


2 houses are on one side of a street, and 2 on the 
other side. How meted are there on both sides ? 


2 - are on one side of a room, sia 4 on the 
other sl How many are ia on both sides? 


2 and 4 are how many ! rf 


Suppose 2 hats are in one place, and 5 in another; » 
how many will there be, if we put them reer: ? 


2 and 5 are how many 3 ? 


_ ‘There are 2 lamps on one side of a table, and 7 on 
~ “the other side. How many lamys are there in all ? 


i TY) i fies 


2 and 7 are how many? 


Charles found 2 chestnuts under one tree, sate 8 
under another. How many did he find in all ? 


2 and 8 are how many? 


Recite the table that begins, T'wo and one are three. 


2 and 1 are and 6 are 8 
2 and 2 are and 7 are 9 
2 and 3 are and 8 are 10 
2 and 4 are and 9 are il 
2 and 5 are and 10 are 12 


‘10 ADDITION. — - 


Lesson T'uinp.~ III. 


3 birds are on one branch of a grape-vine, and 2 on 
another branch. How*many are on both branches? w 


3 ands? are how many ? 


3 boys are standing to recite, and 3 otherg,are com- 
ing to recite with them. How many will there be? 


3 and 3 are how many? 


William noweewns 3 fish-hooks: if he should buy 
6 morertike them, how many would = then have ? 


Jud | 


3 and 6 are how many? 


Jane put 3 pins into a cushion, and Lucy ae in 9 
more. How many were there in the cushion then? 


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fs ss . 3 and 9 are how many? 

‘Tell me how ae Hee are 3 balls and 10 balls ? 
260 20000000000 
3 and 10 are how many? 

Recite the table that begins, T'hree and one are four. 


3 and 1 are 4 ‘3 and 6 are 9 
3 and 2 are 5 a and. = feate. 10 
3 and. 3 are 6 “3 and &-are 11 
> 3 and 4 are 7 3 and 9 are 12 
> 3 and 5 are 8 ‘3 and 10 are 13 
ae: 
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ip. * 


-— 11 

Lesson FdUrtTH. IV. ~ 
In a pond there are + Bees swimming one way, 
and 3 another way. How n ny are there in all? 
re Se SY Sy * Pe 7 


4 and 3 are how many? 
Charles has 4 tame squirrels, and his brother has 
4 miorton: many have they both together? 


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ny? 
4 jugs are on one end of a shelf, and 5 are on the 
other end. How many are there on both ends? | 


“e008 oot 


4 and 5 are how many? 


Sy Sey, 


BAA ae. “Saag 
4 and 4 are how ma 


Here are 4 jars filled with honey, and 6 mire “filled 
_ with jelly. How many are there of them all? 


mt 
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4 and 6 are how many: 


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another man. How many did he sell to the 


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and 7 are how many ?, 


Recite the table that begins, Four and one are five. 


4 and 1 are 5 ‘4 and 6 are 10 
4 and 2 are 6 4-and: 7 are 
4 and 3 are 7 4 and 8 are 12 
4 and 4 are 8 4 and 9 are 13 
4 5 9 4 and 10 


“Or 


12 oe 
Lesson Firtn. V. 
Here are 5 little girls singing together, and 2 more 
are jumping rope. How ADY Ok there in all? | 


5 antl 2: are hier tne 


A gunsmith sold 5 guns to a hunter, and'8 moye to 
a fowler. How many guns did he sell them both? 


CGE ME 


5 and 3 are how many? 


Luther found 5 eggs in one nest, and ee found ~ 
4 in another nest. How many did they both find? - 


SSOOSOD C8SOO0,. 


5 and 4 are how many? 


Here are 5 tops spinning in one row, and 5 more 
in, another row. How: @ € are there in all? 


89999 99S 


gh 9 are how Se ? 


Here are 5 keys for trunk locks, and 6 keys for 
desk locks. How many are there in the whole? 


BELLE LELULE 


and 6 are how many? 


Recite the table that begins, Five and one are six. 


and 6 are 11 
and 7 are 12 
and 8 are 13 
and 9 are 14 
and 10 are 15 


and 1 are 6 
and 2 are 7 
and 3 are 8 
and 4 are 9 
and 5 are 10 


CULO NON 
Sh Ro oy oy 


ADDITION. 13 
LESson SixtTH. VI. 


6 pear-trees are standing in a row, and 2 more are 
ence near them. How many are there j in all? 


* 6 and 2 are how many : ? 
6 robins were on the ground, and 3 more have 
lighted near them. How many are there in all? 


6 and 3 are how many i 


An Indian shot 6 arrows at partridges, and 4 at 
wild turkeys. How many arrows did he shoot away? 


SPELLS. FESO 


6 and 4 are how many? 


A trader sold 6 shovels to a well-digger, and 5 
more toa farmer. How many did he sell to both ?. 


bbibbdbd 


6 and 5 are how many 3 ? 


There are 6 vials filled with one kind of: medicine, 
and 6 with another. How many are there in all ? 


GHDGHt CObbed 


6 and 6 are how many * 
Recite the table that begins, Six and one are seven. 


6 and 1 are 7 6 and 6 are 12 
6 and 2 are 8 G and 7 are 13 
6 and 3 are 9 6 and 8 are 14 
6 and 4 are 10 6 and 9 are 15 <a 
6 and 5 are 11 6 and 10 are 16 
| B 
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14 ADDITION. 


Note to Teachers. In all the preceding Jessons in addition, the learners 
nave been enabled to obtain their answers by counting the pictures of the 
objects embraced in the questions ; and if they have obtained any conception 
of the addition of abstract numbers, the acquirement has been incidental. 
The subsequent exercises, however, will render this acquirement more 
certain. In the following lessons, the numbers embraced in the questions are 
represented by nit marks ; and the teacher must direct the learners to count 
these marks, as they have heretofore counted the pictures. 


Lesson Seventu. VII. 


If you had 7 nuts in one pocket, and 2 in the other, 
how many would you have in both pockets? 


7 and 2 are how many? 


Stephen put 7 pins into a pin-box, and Henrietta 
put in 3 more. How many did they both put in? 


7 and 3 are how many? 


If you had 7 pins on one sleeve, and 4 on the other, 
how many would you then have on both sleeves ? 


7 and 4 are how many? 


John gave 7 apples for a picture, and 5 more fora 
new book. How many apples did he give for both? 


7 and 5 are how many? 


Joseph had 7 marbles, and his brother James gave 
him 6 more. How many marbles had Joseph then? 


7 and 6 are how many? 


Recite the table that begins, Seven and one are eight. 


7 and l are 8 and 6 are 13 
7 and 2 are 9 and 7 are 14 
7 and 3 are 10 and 8 are 15 


7 and 4 are 11 and 9 are 16 
7 and 5 are 12 and 10 are 17 


ADDITION. 15 


Lesson EientuH. VIII. 


James gave 8 quills for a bow, and 2 quills for an 
arrow. How many quills did he give for both? 


S and 2 are how many? 


8 boys are on one end of a form, and 3 on the 
other end. How many are on the whole form ? 


8 and 3 are how many? 


Harriet owns 8 story-books, and 4 school-books. 
How many books does Harriet own of both kinds? 


8 and 4 are how many? 


Susan has 8 plums, and George has 5. If George 
give his to Susan, how many will she then have? 


8 and 5 are how many? 


Richard has 8 white marbles, and Francis has 6. 
How many will there be, if they put them together ? 


8 and 6 are how many? 


Caroline and Frances recited a lesson in arithmetic 
together ; Caroline answered 8 questions, and Frances 
answered 7. How many did they both answer? 


8 and 7 are how many? 


Recite the table that begins, Hight and one are nine. 


8 and 1 are 9 and 6 are 14 
8 and 2 are 10 and 7 are 15 


8 and 3 are ll and 8 are 16 
8 and 4 are 12 and 9 are 17 
8 and 5 are 13 and 10 are 18 


16 ADDITION. 


Lesson Nintu. IX. 


If I put 9 books down im a pile, and you put on 2 
more, how many books will there be in the pile > 


9 and 2 are how many? 


There were 9 plums under the tree, and Henry 
shook off 3 more. How many were there then? 


9 and 3 are how many? 


If I pull out 9 quills from a bunch, and then pull 
out 4 more, how many shall I have taken out? 


PETTEEGdd Til 
9 and 4 are how many? 


There is a class of @ boys, and 5 girls, studying 
arithmetic. How many are there in the class? 


9 and 5 are how many? 


A fisherman caught 9 fishes in a net, and*6 more 
with a hook. How many did he catch in all? 


‘ 


“9 and 6 are how many ? 


Horatio and Edmund keep their books upon the 
same shelf. Horatio has 9 books, and Edmund has 
only 7, How many books have they together? 


9 and 7 are how many? 
Recite the table that begins, Wine and one are ten. 


9 and ‘1 are 10 9 and 6 are [5 
9 and 2 are 11 9 and 7 are 16 
9 and 3 are 12 9 and 8 are 17 
9 and 4 are 13 9 and 9 are l8 
9 and 5 are 14 9 and 10 are 19° 


ADDITION. 17 


Lesson T'entTH. X. 


If I should call 10 boys up to the desk, and then 
should call 2 more, how many would be called ? 


10 and 2 are how many? 


William had 10 marbles, and, returning from 
school, he found 3 more. How many had he then? 


10 and 3 are how many? 


10 boys were going to school, and overtook 4 more 
How many were there going to school together ? 


10 and 4 are how many? 


In a fruit-basket there were 10 red apples, and 5 
yellow ones. How many were in the basket? 


10 and 5 are how many? 


In ahen-coop there are 10 white hens, and 6 black 
ones. How many of both colors are in the coop? 


10 and 6 are how many? 


James has a new jacket, trimmed with bright but- 
tons; and there are 10 of these buttons on each side. 
How many are on both sides, counted together? 


PPTTTEEEEE TPPPPridel 
10 and 10 are how many? 
Recite the table that begins, J’en and one are eleven. 
10 and 1 are 11 10 and 6 are 16 


10 and 2 are 12 10 and 7 are 17 
10 and 38 are 13 10 and 8 are 18 


10 and 4 are 14 10 and 9 are 19 
10 and 5 are 15 10 and 10 are 20 


B2 


-13 SUBTRACTION. 


SUBTRACTION. 
Note to Teachers. Here explain to the learners, that the cipher ed 


represents nothing of itself, being used only to occupy a place. Also, lea 
them to observe the correspondence between addition and subtraction. 


Lesson First. I. 
There was 1 pitcher on the table, but a careless 


=< 


I talken from where there was 1, leaves what ? 


2 trees stood near by, but the wind has blown 3} 
of them down. What number is left standing? 


1 taken from 2, leaves what number ? 


3 chairs were standing in a row, but a child has 
thrown 1 of them down. How many are upright? 


IES 


I from 3 leaves how many? 


7 sugar-loaves are on a shelf; one of them has the 
top broken off. How many of them are whole ? 


440 4 4 


1 from 7 leaves how many ? 


Recite the table beginning, Ore from one leaves nothing. 


1 from Tt leaves O 1 frony 6 leaves 5 
1 from 2 leaves |} 1 from 7 leaves 6 
1 from 3 leaves 2 1 from 8 leaves 7 
1 from 4 leaves 3 || 1 from 9 leaves 8 
1 from 5 leaves 4 1 from 10 leaves 9 


SUBTRACTION. *9 


Lesson Seconp. Il. 


Henry attempted to roll 3 hoops at once, but 2 of 
them have fallen down. What number is still up? 


2 from 3 leaves what number ? 


5 boys came up to recite, but 2 of them were sent 
back for having no lessons. How many recited? 


2 us 5) Race fos many : 2 


Here are 6 cherries, 2 of which have lost off their 
stems? JIfow many are there with stems on? 


—e--6 —@ @6 ® 
2 from 6 leaves how many? 


7 bottles were standing on a table, but 2 of them 
are turned down. How many are still upright? 


BGO 00 oom 


2 from 7 leaves how many ? 


Here are 8 pitchers, and 2 of them are placed 
bottom upward. How many are Ris ciad side up? 


2 from 8 leaves how Pairs 


Reeite the table beginning, Two from two leaves nothing. 


2 from 7 leaves 5 
2 from 8 leaves 6 
2 from ® leaves 7 
2 from 10 leaves 8 
2 from 11 leaves 9 


2 leaves 
2 from 3 leaves 
2 from 4 leaves 
2 from 5 leaves 
2 from 6 leaves 


20 SUBTRACTION. 
Lesson T'uirp. III. 


A tobacco-smoker, having 5 pipes, has broken the 
stems off of 3 of them. How many remain whole? 


eS SR PROS: 5 ae 


3 from 5 leaves how many? 


6 hens were eating corn, and a boy frightened 3 of 
them away. How many of them remained? 


3 f Soin 6 pe how many ? 


There were 7 farmers, 3 of whom drank rum and — 
whisky, and became miserable; the rest drank water, 
and were healthy and happy. How many drank water ? 


3 fori 7 leaves how ay 


8 bowls are on a table, and 3. of them are turned 
bottom upward. How many are right side up? 


SSCS 97444 


3 from 8 edes how many? 


A silversmith has made 9 thimbles; now, if he 
sell 3 of them, how many will he have left? 


BB RR & & we @ @ 


3 from 9 leaves how many? 
Recite the table beginning, Three from three leaves nothing. 


3 from 3 leaves 0 3 from 8 leaves 5 
3 from 4 leaves 3 from 9 leaves 
3 from 10 leaves 


1 6 
3 from 5 leaves 2 7 
3 from 6 leaves 3 3 from 11 leaves 8 

4 9 


3 from 7 leaves 3 from 12 leaves 


SUBTRACTION. Qh 
Lesson Fourtrn. IV. 


In a certain yard there are 6 sheep; 4 of them 
have -aiad down to rest. How many are standing? 


=f 

SSS GES 
a 4 S ee é REST le Coa f ee ‘ 
a, Mie ve : Kies it Ness Se Sees = mye: : 
4 from 6 leaves how many ? 


Here are 7 umbrellas; 4 of them are open, and the 
rest are shut. How many of them remain shut? 


4 from 7 leaves how many? 


Here are 8 water-yails, 4 of which have lost their 
handles. How many remain with handles on ? 


4 orn 8 leaxes how many? 


9 cricket seats were standing in a row, but 4 of 
them are upset. How many are still standing ? 


: in 9 leaves how many ? 


Augusta has’ ane pins, but 4 of them have lost off 
their heads. How many have their heads on? 


Mee ALA LF. 


4 fiom 11 leaves how many? 


Recite the table beginning, Four from four leaves nothing. 


4 from 4 leaves 4 from 9 leaves 5 
4 from 5 leaves | 4 from 10 leaves 
4 from 6 leaves 4 from 11 leaves 


4 from 7 leaves 4 from 12 leaves 
4 from 8 leaves 4 from 13 leaves 


29 SUBTRACTION. 


Note to Teachers. Wearners will generally diseover the correspondence 
of addition and subtraction. It will be well, however, for the teacher to 
imvress the correspondence of these two operations, by frequently proposing 
questions, thus, —‘ Five and how many make eight ?— Then three from 
eight leaves how many ?’ 

‘The learners must be informed, that the unit marks which are inclined 
represent the number to be subtracted, and those which are upright show the 
number that will remain. 


Lesson Firrn. YV, 


Robert had 7 nuts in his pocket, but he lost out 5 
of them. How many of them then remained ? 


L1///7/7/ 
5 from 7 leaves how many? 


‘Thomas put 8 chestnuts into the: embers to roast, 
but 5 of them burnt up. How many were saved? 


LLL S/S7/7/ 
5 from 8 leaves how many? 


9 boys were playing ball, but 5 of them became 
tired, and went home. How many remained? 


PELE SS 77/7 
5 from 9 leaves how many ? 


Charles had 10 marbles, and he gave his brother 
John 5 of them. What number had he left? 


PETEL///77/ 
5 from 10 leaves how many ? 


A hen had 11 little chickens, but the rats caught 5 
of them. How many of them then remained ? 


PLT EEL 77/77 


5 from 11 leaves how many ? 


Recite the table beginning, Five from five leaves’ nothing. 


5 from 10 leaves 
5 from 11 leaves 
5 from 12 leaves 
5 from 13 leaves 
_5 from 14 leaves 


5 from 5 leaves 
5 from 6 leaves 
5 from 7 leaves 
5 from 8 leaves 
5 from.9 leaves 


m C2 WO © 
{OoDOntAau 


SUBTRACTION. O93 
Lesson Sixtru. VI. 


I placed 7 books upright on a shelf, but 6 of them 
have fallen down. What number remains upright ? 


|////441 
6 from 7 leaves what number ? 


There were 8 chairs in a room, but 6 of them have 
been carried out. How many remain in the room ? 


LI /////7/ 
6 from 8 leaves how many? 


9 birds lighted on a tree, but a little dog frightened 
off 6 of them. How many then remained? 


LL S///77/ 
6 from 9 leaves how many ? 


’ If a farmer who has 10 cows should sell 6 of them, 
how many cows would he then have remaining ? 


PELL S7/7/7/7 
6 from 10 leaves how many? 


Joseph bought 11 quills, but he lost 6 of them 
while going home. How many had he left? 


LT LEE 7/777 
6 from 11 leaves how many? 


There were 12 little girls in a certain class, but 6 
of them neglected their lessons, and were put out of 
the class. How many remained in the class? 


PT LELILSSS777 | 


_ 6 from 12 leaves how many? 


Recite the table beginning, Sir from six leaves nothing. 


6 from 6 leaves 0 6 from 11 leaves 5 
6 from 7 leaves 1 6 from 12 leaves 6 
6 from 8 leaves 2 . 6 from 13 leaves 7 
6 from 9 leaves 3 6 from 14 leaves 8 
6 from 10 leaves 4 6 from 15 leaves 9 


84 SUBTRACTION. 
Lesson Seventu. VII. 


A trader bought 9 barrels of flour, and sold 7 of 
them. How many had he then remaining ¢ 


LE SSSS S77 


7 from 9 leaves how many? 


10 boys ran a race in the wind, and 7 of them lost 
off their hats. How many saved their hats on? 


LIE SSS S/S 7/7 


7 from 10 leaves how many? 


11 doves were picking up oats in the yard, anda 
dog drove off 7 of them. How many remained ? 


LITLE SSS S/S 7/7 


7 from 11 leaves how many ? 


Henry’s pear-tree had 12 blossoms on it ; 7 of them 
dropped off; the rest ripened. How many ripened ? 


LETTE SSS 77/7 


7 from 12 leaves how many? 


Stephen received 13 quills, and gave away 7 of 
them for paper. How many had he remaining ? 


PPLE LE 7/4/7777 


7 from 13 leaves how many? 


14 boys started to go to school together; but 7 of 
them went off in a boat, and were upset, and drowned. 
How many of them went safely to the school? 


LP TETEL SSS 7777 


7 from 14 leaves how many? 


Recite the table beginning, Seven from seven leaves nothing. 


7 from 0 7 from 12 leaves 5 
7 from 8 leaves ] 7 from 13 leaves 6 
7 from 9 leaves 2 7 from 14 leaves 7 
7 from 10 leaves 3 7 from 15 leaves 8 
7 from 11 leaves 4 7 from 16 leaves 9 


7 leaves 


SUBTRACTION. Q5 
Lesson Erentu. VIII. 


9 boys were in a stage-coach, and 8 of them were 
turned out for being noisy. How many rode on? 


LS/S/S//111 


8 from 9 leaves how many ? 


Joseph had 10 sheets of paper, but he has sold 8 
sheets. How many sheets has he remaining? 


LESSS///717 


8 from 10 leaves how many? 


If I had 11 pens, and I should give you 8 of them, 
how many pens should I then have remaining ? 


LLL SS7// 7/77 


8 from 11 leaves how many? 


12 pears grew upon a little pear-tree, and 8 of them 
have dropped off. How many are still on the tree? 


LTTE SSS 7/777 


8 from 12 leaves how many? 


A ship’s crew consisted of 13 men, and 8 of them 
died while at sea How many arrived safe in port? 


LLL LE S/S7777/77/ 


8 from 13 leaves how many? 


In a certain class there were 14 scholars; 8 of them 
were thoughtless and idle; the remainder were very _ 
good scholars. How many were good scholars? wilt. 


PTTL IISS/77777 
8 from 14 leaves how many? 
‘Recite the table beginning, Eight from eight leaves nothang. 
8 from 8 leaves 8 from 13 leaves 


8 from 9 leaves | 8 from 14 leaves 
8 from 10 leaves 8 from 15 leaves 


8 from 11 leaves 8 from 16 leaves 
8 from 12 leaves 8 from 17 leaves 


26 SUBTRACTION. 
Lesson Nintru. IX. 


12 boys had leave to go out and play, but only 9 
of them chose to go. How many remained in? 


PLE SSSSS// 77 


Stephen bought 14 quills, and in writing he has 
used 9 of them. How many has he remaining ? 


PET EE SSS 777/77 


John got 15 quills, and lost 9. How many remain ? 


PEELE S47 77/777 


Recite the table beginning, Vine from nine leaves nothing. 


9 from 9 leaves 0 9 from 14 leaves 5 
9 from 10 leaves 1 9 from 15 leaves 6 
9 from 11 leaves 2 9 from 16 leaves 7 
9 from 12 leaves 3 9 from 17 leaves 8 
9 from 13 leaves 4 9 from 18 leaves 9 


Lesson T‘entTH. X. 


James had 12 peaches given him, and he gave 10 
of them to his mother. How many had he left? 


LESSSSAS SSS 


Tiucy put 15 pins in a cushion, and then took out 10 
of them. What number remained in the cushion ? 


te PELELSSSSSS S777 


Ann had 17 pins, and lost 10. How many remained ? 


© FRELELLS477777777 


Recite the table beginning, Zen from ten leaves nothing. 


10 from 10 leaves O 10 from 15 leaves 5 
10 from 11 leaves 1 10 from 16 leaves 6 
10 from 12 leaves 2 10 from 17 leaves 7 
10 from 13 leaves 3 10 from 18 leaves 8 
10 from 14 leaves 4 10 from 19 leaves 9 


QP ae *“ a * Co ee ee sd 


MULTIPLICATION. 27. 


MULTIPLICATION. 


Lesson First. I. 


A father promised his son a new book for every time 
he recited correctly, during the week. The week 
passed on, and the boy recited correetly only once. 
What number of books did he receive? 


Once 1 is what number? 


Charles caught 1 fish every time he went out to 
angle. How many did he catch in going 2 times? 


ore 


2 times 1 are how many? 


A young cooper worked 3 days, and made 1 barrel 
each day. How many barrels did he make in all? 


- < 


4 times I are how many? 
Recite the table that begins, Once one is one. 


Once lis. 1 6 times 1 are 6 
2 times*I are 2 7 times l are 7 
3 times l are 3 8 times lare 8 
4 times l are 4 9 times l are 9 
5 times | are 5 10 times 1 are 10 


28 MULTIPLICATION. 


Lesson Seconp. II. 
A boy has 2 hands :— how many hands have 2 boys? 


—— 2 =e a 
2 times 2 are how many ? 


A rabbit has 2 ears: — how many ears have 3 rabbits ? 


3 times 2 are Loy nial? 


James caught 2 fishes every time he went a fish- 
img. How many ag he catch in going 4 times ? 


4 times 2 are how many ? 


If 1 desk have 2 keys, how many keys have 5 desks? 


SS SS HS 


5 times 2 are how many? 


Harriet lost 2 pins every time she-went to school. 
Now, how many did she lose in going 7 times ? 


l ek Le 


7 times 2 are how many? 


Recite the table that begins, Once two is two. 


Once 2 is 2 6 times 2 are 
2 times 2 are 4 7 times 2 are 
3 times 2 are 6 8 times 2 are 
4 times 2 are 8 9 times 2 are 
5 times 2 are 10 10 times 2 are 


MULTIPLICATION. 29 


Lesson 'l'uirp. III. 


Once 3 is how many? 


If one stand have 3 legs, how many have 2 stands ? 


——=— ‘eo 


) 


2 times 3 are how many? 


When Henry was learning to write, he used 3 
quills a week. How many did’ he use in 3 weeks? 


Ws fi fo 


3 times 3 are how many? 


If one fork have 3 points, how many have 4 forks? 


Ce 87% F. 


4 times 3 are how many? 


Once 3 is 3 6 times 3 are 18 

2 times 3 are 6 -T times 3 are QI 

a 3 times 3 are 9 8 times 3 are 24 
_ | 4 times 3 are 12 9 times 3 are 27 
- |  5-times 3 are 15 10 times 3 are 30 


me Oe 
Pn C.2 
‘er es “as 
, ne ~ £ 
wk ted Te a Bam a 


30 MULTIPLICATION. 


Lesson Fourth. IV. 


2 school-houses are so placed, that we see 4 win 
dows in each. How many do we see in both? 


2 times 4 are how many? 


3 horses are trotting off without riders. Each 
horse has 4 feet. How many feet have they all? 


ee Dy 


Won 


3 times 4 are how many ! 2 
A crib has 4 legs : —how many legs 1 4 cribs ? 


} <q TO, 
TTA + a FTRPELATUFETATEE q Tana : 
] } 


4 times 4 are how many? 
Here are 5 chairs : —how many legs have they all ? 


yh oh hh hh Th 


5 times 4 are how many? 


Here are 6 short ladders, each ladder having 4 
rounds. How many rounds are there im all ? 


Oe Fes Ae 


6 times 4 are how many ? 


Recite the table that begins, Once fowr is: four. 


6 times 
7 times 4 are 
8 times 4 are 
9 times 4 are 
10 times 4 are 


Once 
2 times 4 
3 times 4 
4 times 4 are 16 
5 times 4 


MULTIPLICATION. 3} 


Lesson Firtn. Y¥. 


If 2 boys, that have 5 books apiece, should put 
their books together, how many would there be? 
‘To learn the answer, you may count these balls. 


2 times 5 are how many? 


Luey gets 5 merit-marks every time she recites. 
How many does she get in reciting 3 times? 


3 times 5 are how many ? 


A lady, who had 4 daughters, gave each of them 5 


books. What number did she give them all ? 
6e ee ee 6e 
e300 e800 888 600 


4 times 5 are how many ? 


Sarah reads 5 pages of history every mornmg. 
How many pages does she read in 5 mornings? 


5 times 5 are how many? 


If you get 5 merit-tickets every week, for perfect 
lessons, how many can you get in 6 weeks? 


6 times 5 are how many? 


If Joseph should perform & lessons every day, how 
many lessons would he perform in 7 days? 


% times 5 are how many? 


‘s 


Recite the table that begins, Onee five is five. 


6 times 5 are 
7 times 5 are 
8 times 5 are 
9 times 5 are - 
10 times 5 are- 


Once 5 is 5 
2 times 5 are 10 
3 times 5 are 15 
4 times 5 are 20 
5 times 5 are 25 


82 MULTIPLICATION. 


Lesson SixtnH. VI. 


Little Charles has had 2 picture-books given to 
him; and in each book there are 6 pictures. How 
many pictures are there in both of the books ? 


2 times 6 are how many? 


3 wagons went to market, carrying 6 barrels of 
flour apiece. How many did they all carry? 


©@6 866 8680 
@86 660 620 


3 times 6 are how many? 


’ There are 4 wire cages, in each of which there are 
6 birds. How many birds are there in all? 


©8060 690 6808060 6693 
@60 6690 68693 e096 


4 times 6 are how many? 


If a clerk in a book-store use 6 quills in one week, 
what number of quills will he use in 5 weeks? 


220 ©2998 692 686 628 
©9309 6908 886 G68 e680 


5 times 6 are how many? 


If you answer 6 questions in reciting once, how 
many will you answer in reciting 6 times? 


@€838 699 80080 e680 83030 6886 
6839 ©6080 6@960 620 689 666 


6 times 6 are how many? 


A fishing-party went off in 7 boats, and each boat 
carried 6 men. How many went in the party? 


2806 6063 069930 66959 €8080 689083 889 
669 ©0806 66020 G20 6890390 6600 6690 


7 times 6 are how many? 


Recite the table that begins, Once six is siz. 


Once 6 is 6 6 times 6 are 36 


2 times 6 are 12 7 times 6 are 42 
3 times 6 are 18 8 times 6 are 48 
4 times 6 are 24 9 times 6 are 54 
5 times 6 are 30 10 times 6 are 60 
~ 


MULTIPLICATION. 33 


Lesson Sreventu. VII. 


Suppose a scholar should answer 7 questions in 
withmetic every time his class recites ;——-how many 
juestions would he answer in reciting once? 


Once 7 is how many? 


If you had 7 nuts in each of your 2 hands, how 
many would you have, counting them together ? 


2 times 7 are how many? 


If I give you some raisins 3 times, giving you 7 in 
number each time, how many will you receive ? 


3 times 7 are how many? 


If 4 boys stand up to read, and each boy read 7 
ines, what number of lines will. they all read ? 


4 times 7 are how many? 


If you give 7 apples for one sheet of letter-paper, 
how many apples must you give for 5 sheets? 


5 times 7 are how many ? 


Suppose a boy to give 7 chestnuts for one .apple ; 
how many chestnuts must he give for 6 apples? 


6 times 7 are how many ? 


7 


Recite the table that begins, Once seven is seven. 


Once 7 is q 6 times 7 


2 times 7 are 14 7 times 


7 
3 times 7 are 21 S times 7 
4 times 7 are 28 9 times 7 
5 times 7 are 35 10 times 7 


34 MULTIPLICATION. 


Lesson Ereuru. VIII. 


If a hunter should shoot 8 foxes every time he 
went out into the woods a hunting, what number of 
foxes would he shoot by going out once? 


6969 
S309 


Once 8 is how many? 


If there be 8 leaves in one writing-book, how 
many leaves will there be in 2 writing-books ? 


6800 2€8990 
®336 6990¢e 


2 times 8 are how many? 


Stephen was 8 weeks in this book, and James was 
3 times as long. How long was James in it? 


CSCS 6836060 C666 
@6SS6 8699 6666 


3 times 8 are how many? : 


How many roses may be gathered from 4 rose- 
bushes; allowing each bush to bear 8 roses? 


82668 83660 0688399 29839 
SS6¢3d 62330 889693 9039 


4 times 8 are how many? 


If 8 boys can sit upon one form, what number of 
boys can sit upon 5 forms of the same length? 


GECS S366 E2609 6068090 63689 
©5960 C959 C890 GSES 8969 


5 times 8 are how many? 


How many oranges can you put into 6 fruit-bas- 
kets; allowing each basket to contain 8 oranges? 


€8Hé6 G2660 e699 S230 @308¢S9 66690 
G66SSo 6893S 89639 26020 68330 662¢0 


6 times 8 are how many? 


Recite the table that begins, Once eight is eight. 


Once 8 is 8 6 times 
2 times 8 are 16 7 times 8 are 
3 times S are 24 8 times 8 are 64 
4 times 8 are 32 9 times 8 are 72 ‘ 
5 times 8 are 40 8 are 80 


10 times 


MULTIPLICATION. 3D 


Lesson Nintu. IX. 


If 9 persons can ride inside of one stage-coach, 
how many can ride inside of 2 stage-coaches? 


e809 e300 
eee2o ©6609 


3 men went out a fox-hunting, and each man 
caught 9 foxes. How many did they all catch? 


@eoe S$@es @8¢6 
@89ee6 @S6e0 ©8eeoso 


If one boy eat 9 plums, how many will 4 boys eat? 


@96¢9 - C868 C©eee@ @900 
Sees9o GESse@ 6eee2o0 @6¢eoe0 


Recite the table that begins, Once nine is nine. 


| Once 9 is 9 6 times 9 are 54 


2 times 9 are 18 7 times 9 are 63 
3 times 9 are 27 8 times 9 are 72 
4 times 9 are 36 9 times 9 are 81 
5 times 9 are 45 10 times 9 are 90 


Lesson T'entTH. X. 


James has had 10 new books, and Caroline has had 
twice as many. How many has Caroline had? 


62009 _ 86009 
6060 § @6¢00e 


Edward has 3 jackets, and on each jacket there are 
10 buttons. How many buttons are there on all? 


If one box hold 10 hats, how many will 4 boxes hold? 


@eeeo eees9 032800 @eee0 
©6390 @eeee ©2800 eesee 


Recite the table that begins, Once ten is ten. 


Once 10 is 10 6 times 10 are 60 


2 times 10 are 20 7 times 10 are 70 
3 times 10 are 30 8 times 10 are 8&0 
4 times 10 are 40 9 times 10 are 90 


‘ ‘| 5 times 10 are 50 10 times 10 are 100 


360 DIVISION. 


DIVISION. 


Note to Teachers. The correspondence of Multiplication and Division, if 
not discovered by the learners, should be pointed out by the teacher. 


Lesson First. MI. 


When Nathaniel was sick, one of his school-mates 
brought 4 grapes to him; but his physician said, 
be must eat only one at a time. How many times 
could he have 1, before they would all be gone? 

@eeeo 


~_——_—— — 


How many times 1 are there in 4? 


If a man catch 1 fish every time he goes out a fish 
ing, how many times must he go out to catch 6? 
@@e@e0e00 


~———Se 


How many times | are there in 6? 


A certain farmer has 4 oxen, and it takes 2 of them 
to make a pair. How many pairs of oxen has he? 
@00e0 


JF 
How many twos are there in 4? 


Asa can carry 2 sticks of wood at once; and he has 
6 sticks to carry off. How many times must he go ? 
ee0e0e8 
SS ed 
How many times 2 are there in 6? 
John gets up 2 places in his class every day. In 
how many days will he get above 8 scholars? 
@e2e0200000 
FAS RF NS 


How many times 2 are there in 8? 


Recite the table that begins, T'wo in two, once. 


in 12, 6 times. 
in 14, 7 times. 
in 16, 8 times. 
in 18, 9 times. 
in 20, 10 times. 


in 2, once, 

in 4, 2 times. 
in 6, 3 times. 
in 8, 4 times. 
in 10, 5 times. 


WNW NW NW 
WwW WWW 


DIVISION. 37 


Lesson Seconp. II. 


Robert had 6 baskets to carty into the field, and 
he could carry only 3 at a time. How many times 
had he to go, in order to carry off the whole? 

®©0ee0e0 
ae a eee 


= 
¥ 


How many times 3 in 6? 


If here were 9 books, how many times could I 
take off 3 books, before they would all be gone? 
@e0e000000 
Nee OY OS 
How many times 3 in 9? 

If a gunner shoot 3 plovers every time he fires, 
how many times must he fire, to shoot 12 plovers ? 
@0000808060000690 
NS ON NT 
How many times 3 in 12? 

Laura gets 3 merit-marks for every perfect lesson. 
How many lessons must she recite, to get 15 marks ? 
©0200 OCOCOOCOCECCE 
How many times 8 in 15? 

Suppose 3 books are required to supply one scholar, 
how many scholars may be supplied from 18 books ? 
@e00000666000000000 
ee Ne ee se Goes es 
How many times 3 in 18? 
If a boy can get one pine-apple for 3 oranges, then 
how many pine-apples can he get for 21 oranges? 
How many times 3 in 21? 


Recite the table that begins, Three in three, once. 


3 in 3, once. 3 in 18, 6 times, 
3 in 6, 2 times. 3 in 21, 7 times. 
3 in 9, 3 times. 3 in 24, 8 times, 
3 in 12, 4 times. 3 in 27, 9 times, 
3 in 15, 5 times. 3 in 30, 10 times. 


— 


38 DIVISION. 


Lesson: T uirpe.- IL: 


There is a market woman that has 8 apples, and 
for every 4 of them she can get one large orange. 
How many oranges can she get for all her apples? 

@@@e80096 
Ne Ne 
How many times 4 in 8? 


lf here were a fruit-basket with 12 oranges in it, 
how many times could you take out 4 oranges? 
©80968080800 
SS ee A | 


How many times 4 in 12? 


If it take 4 sheets of paper to make one copy-book, 
how many copy-books can be made of 16 sheets? 
Geeesedoeseecesneo 
aE PES 5S et ee aS eee 
How many times 4 in 16? 


If it take 4 horses to draw one stage-coach, how 
many stage-coaches can be drawn by 20 horses? 
G6@6@000698960603900669 


ee ee eS 


How many times 4 in 20? 


24 boys, that stood in a line, were asked, how many 
times 4 boys there were of them. You may tell. 
©608860288906680809000000868 
AE Oa aS REE ES ig |, RL Uh LE al a SP an pa ere ee pg, a Te OEY | 
How many times 4 in 24? 
Emeline’s new picture-book contains 28 leaves 


How many times 4 leaves are there in the book? 
OGSGGoodCSGSSSOodeOGGGGOoeseods 
Nearest Cc Nee Nene Na ceociee 


How many times 4 in 28? 


Recite the table that begins, Four in four, once. 


4 in 4, once. 4 in 24, 6 times. 
4 in 8, 2 times. 4 in 28, 7 times. 
4 in 12, 3 times. 4 in 32, 8 times. , 
4 in 16, 4 times. 4 in 36, 9 times. . 
4 in 20, 5 times. 4 in 40, 10 times. : 
= Ap green. 
\ ee eae eS 


DIVISION. 39 


Lesson Fourrnu. IV. 


The first class of a certain school contains 15 
girls. How many times 5 girls are in the class? 
O©S@eeseeseoeoesos esse 
a ee ee 


a 
If you write 5 lines in a writing-book, every day, 
how many days will it take you to write 20 lines ? 
S9@e@eseseeesesseo6SGS5S3689 
bE DE eee eS SS ie, ee ees Ie, Senne Le eee 


In a book of 25 leaves, how many times 5 leaves? 
GSSSSVSSCSSOSSSESSSCTSSOZSESCCS 
Se 


a eT i i A ce ag in RS Ne ee a a) 


Recite the table that begins, Five in_five, once. 


in 5, once. 

in 10, 2 times. 
in 15, 3 times. 
in 20, 4 times. 
in 25, 5 times. 


in 30, 6 times. 
in 35, 7 times. 
in 40, 8 times. 
in 45,° 9 times. 
in 50, 10 times. 


Orv Orv Or or On 
Orv Orv Or Or Or 


Lesson Firtn.§ V. 


A farmer, who keeps 18 cows, has a separate yard 
for every 6 of them. How many yards has he? 
SOSHLOSSCOSSSSSSSOOES 
pee SR TE, a ei RS NPE BRI AE Re Ee! 5 


There is a school of 24 boys, and 6 boys are in 
each of the classes. How many classes are there? 


OSSSSSOSSSSSssSsesesosGsSESGG 
ta REY ES EB BR SEEM fe, ti rey 


In a school of 30 girls, how many times 6 girls ? 
SSSSGSHSSOSSISSSSSSOSSCSSSVGESSSES 
op I a ae Sa ie SRS i RE “ee et a ee 


Recite the table that begins, Sir in six, once. 


6 in 6, once. in 386, 6 times. 
6 in 12, 2 times. 6 in 42, 7 times. 
6 in 18, 3 times. 6 in 48, 8 times. 
6 in 24, 4 times. 6 in 54, 9 times. 
6 in 30, 5 times. i 10 times. 


40 DIVISION. 


Lesson Sixtn. VI. 


Recite the table that begins, Seven in seven, once. 


in 7, once. 

in 14, 2 times. 
in 21, 3 times. 
in 28, 4 times. 
in 35, 5 times. 


in 42, 6 times. 
in 49, 7 times. 
in 56, 8 times. 
in 63, 9 times. 
in 70, 10 times. 


~) +] +) +] +) 
~t +} +} +} +) 


Lesson Seventu. VII. 


Recite the table that begins, Eight in eight, once. 


once. in 48, 6 times. 
2 times. in 56, 7 times. 


3 times. in 64, 8 times. 
4 times. in 72, 9 times. 
5 times. in 80, 10 times. 


Lesson Eseutu. VIII. 


Recite the table that begins, ine in nine, once. 


9 in 9, once. 9 in 54, 6 times. 
9 in 18, 2 times. 9 in 63, 7 times. 
9 in 27, 3 times. 9 in 72, § times. 
9 in 36, 4 times. 9 in 81, 9 times. 
9 in 45, 5 times. 9 in 90, 10 times. 


Lesson Ninto. IX. 


Recite the table that begins, J’en in ten, once. 


10 in IQ, once. / 10 in 60, 6 times. 
10 in 20, 2 times. 10 in 70, 7 times. 
10 in 30, 3. times. 10 in 80, 8 times. 
10 in 40, 4 times. 10 in 90, 9 times. 

16 in 50, 5 times. 10 in 100, 10 times. | 


“a 


EXERCISES. 41 


EXERCISES IN ADDITION. 


Note to Teachers. Learners, that have been through the preceding lessons 
only once, may return to page 8, and perform the ‘lessons a second time, 
reciting with books closed, before they proceed to the following exercises. 

In the following lessons in Addition, the teacher may embrace each couple 


of numbers in a separate question, thus 3 — ‘9 and 4 are how many ?’ 
Lessons. 

is II. If. LV. 
9 and 4 9 and 6 8 and 6 9 and 5 
6 and 3 8 and | 5 and 3 Tand 3 
8 and 5 6 and 6 10 and 9 4and 4 
2 and 2 10 and 8 S and 8 10 and 3 
10 and 4 5 and 4 6 and 4 Sand 4 
4: anf 8 and 2 9 and 2 5 and = 2 
4 and 1 3 and 2 10 and 6 Tand 4 
9 and 7 9 and 3 oo ape 10 and 5 
5 and 5 7 and 6 Tand 2 Sand 7 
10 and 1 6 and 5 4 and 3 6 and 2 
9 and 8 10 and 2 tT and 5 Sand 3 
4 and 2 9 and 9 10 and 7 10 and 10 


EXERCISES IN SUBTRACTION. 


Note to Teachers. The method of performing these lessons may be 
similar to that adopted in the preceding lessons. ‘fhe teacher may embrace 
each couple of numbers in a question, thus ;—‘3 from 4 leaves how many ?’ 


LEssoNns. 
I. I. IIT. IV. 
3 from 4 8 from 17 8 from 10 5 from 7 
5 from 14 9 from 15 3 from 7 8 from Il 
8 from 8 5 from 8 6 from 14 6 from 10 
10 from 19 7 from 16 2 from 9 7 from 15 
2 from 11 6 from 11 7 from 13 5 from 9 
9 from 18 2 from 8 9 from 17 6 from 13 
4 from 13 | 10 from 14 4 from 6 7 from 11 
9 from 11 8 from 13 7 from 14 | 10 from 16 
4 from 8 6 from 9 3 from 11 3 from 6 
8 from 12 9 from 13 4 from 12 5 from 13 
4 from 9 2 from 6 2 from 5 8 from 16 
3 from 10 5 from 10 4 from 11 3 from 8 
5 from 12 8 from 14 9 from 16 6 from 15 
7 from 9 7 from 12 3 from 9 9 from 14 


42. EXERCISES. 
MULTIPLICATION TABLF. 

AOS PSEC ee 2ST AMA OE 
9 14248 4 4 bf 64-7 | 8] 10g 
Soba |6|8|io|i2| 14] 16| 18 | 208 
Sa [6 | 9/12] a5 |18| a1 | 24 | 27 | a0 9 
oa | 8 [12/16 | 20 | 2 [2s [ae | ag | a0 8 
oS [10 | 15/20/95 | 80| 85 | 40 | 45 | a0 
eG [a2 | 18 | 24 | B0| 80) 42 [as | sa] oo 6 
$7 [aa [ai |as|as|42| 49 | 56 | os | 20 5 


t 
ay pe, ne eS Se ee 
" “f 


& 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 8¥ | 90 4 
o——— -—_- 

* 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | £00 
* pte SR See _ *K 


This table may be used thus — Suppose you wish 
to find how many are 6 times 7; place your finger 
on the 6 that stands in the left hand column ; then 
side the finger to the right till it gets under the 7 
that stands in the top hne;-here you will find 42, 
which is the answer. 


Iidward made a number of. stars upon his slate, 
arranging them so that they appeared im rows two 
ways. Viewing them one way, there were 4 rows 
of 9 stars each; ses ies there were 4 times 9 stars. 
Viewing them the other way, there were 9 rows of 
4 stars each ;—thus, there were § times 4 stars. 


So Edward learned, that 4 times 9, and 9 times 4, are 
just alike. The same is true of any two numbers 


EXERCISES. 43 


EXERCISES IN MULTIPLICATION. 


Note to Teachers. Make two questions on each of the following couples of 
factors, thus ;— ‘3 times 6 are how many ?’” ‘6 times 3 are how many ?’ 


Lessons. 
im El. Il. IV. 
38 times 6] 1 time 8 |! 3 times 5 3 times 7 
5 times 8 | 6 times 6 | 9 times 10 4 times 4 
2 times 2 | 8 times 10 | 8 times 8 | 3 times 10 
4 times 10 | 4 times 5 | 4 times 6 4 times 8 
7 times 7 | 2 times 8 | 2 times 9 2 times 5 
l1 time 4 | 2 times 3 | 6 times 10 4 times 7 
7 times 9 | 3 times 9 | 3 times 3 5 times 10 
5 times 5 | 6 times 7 | 2 times 7 7 times 8 
| time 10 | 5 times 6 | 3 times 4 2 times 6 
8 times 9 | 2 times [0 | 5 times 7 3 times 8 
2 times 4 | 9 times 9 | 7 times 10 | 10 times 10 


EXERCISES IN DIVISION. 


Note to Teachers. ‘The following couples of numbers are to be embraced 


‘n separate questions, thus;—‘ How many times 4 are there in 3617’ 
Lessons. 
I. Il. LIT; LV. 

4 in 36 2 in 16 5 in 35 9 anes FS 
3 in 18 2 in 6 7 in 70 9 in 54 
5 in 40 3 in QT 5 in 45 10 in 80 
Rin .4 6 in 42 3 in 2] 9 in 7 
4 in 40 5 in 30 4 in 16 ffi ts eae: 5. 
7 in 49 2 in 20 3 in 30 Sin 48 
lin 4 9 in SI 4 in 32 9in 18 
7 in 63 G in 48 2 in 10 10 in 60 
& ih.25 3 in 15 4 in 28 7 in 14 
1 in 10 9 in 90 5 in 50 ine do 
8 in 72 8 in 64 7 in 56 9 in 45 
2in 8 4 in 4 2in 18 Wigs ah | 
6 in 54 2 in 18 3 In 24 8 in 32 
lin 8 6 in 60 10 in 70 7 ae 
6 in 36 3 in 9 9 in 36 10 in 50 
8 in 80 2 in 14 6 in I8 8 in 56 
4 in 20 ain 12 9 in 63 10 in 100 


44° DIVISION. 


SUPPLEMENT TO DIVISION. 


Note to Teachers. Division has, thus far, been applied simply to the 
ourpose of finding how many times one number is contained in another. ‘The 
»bjeet now is, to apply Division to the purpose of separating a number into 
« given number of equal parts. 


LESSON. 


A boy had 12 raisins to divide equally among 4 
little girls. He first gave round one raisin to each 
girl, and that took 4 raisins. Now, how many times 
eould he give round one raisin to each girl? Then 
how many raisins would each girl receive? 

If you had 20 raisins to divide equally among 4 
girls, how many times could you give round one 
ypiece to them? ‘Then how many would each girl 
fecelve? How many times 4 are there in 20? 


There is a pile of 15 books to be divided equally 
among 3 boys. If each boy take off one book, how 
many will be taken off? How many times can they 
take off one book apiece? Then how many will 
each boy have? How many times 3 in 15? 


If 18 books be divided equally among 3 boys, how — 
many will each get? How many times 3 in 18? 


In a basket there are 30 apples to be divided equally 
among 6 boys. If they all take out one apple apiece, 
how many will there be taken out? How many times 
can they all take out one apiece? ‘Then how many 
will each boy have? How many times 6 in 30? 

If 42 apples be divided equally among 6 boys, how 
many will each have? How many times 6 in 42? 

3 boys have agreed to make up a pile of 12 books, 
each boy putting on an equal number. How many 

ust each put on? How many times 3 in 12? 

John ate 32 apples in 8 days, eating an equal num- 
ber each day. How many did he eat in one day? 

If you had 30 walnuts to divide equally among 5 
boys, what number would you give to each boy? 

If a school of 56 scholars be divided into 7 equal — 
classes, how many will there be in each class? *. 


MISCELLANEOUS EXAMPLES. 45 


MISCELLANEOUS EXAMPLES. 


Note to Teachers. The books may be open during the recitation of all 
the subsequent lessons, and the questions thay be read either by the scholars 
of by the teacher. Every answer should fully express the process of the 
solution, and the reasoning i# the case. It is, however, essential that the 
learner’s own apprehension should direct him in the process of solution ; 
therefore, hie should not be compelled, nor even allowed to use any form of 
expression that he has not made his own ‘The child’s first etenpie at 
reasoning, however puerile, should be received kindly, and corrected in a 
mauner not likely to destroy his reliance upon his own understanding. 


Lesson First. I. 


1. If a book cost 10 cents, and a pencil cost 7 
cents, how many cents will it take to buy them both ? 
Answer. 10 cents and 7 cents are 17 cents. 


2. There were 16 trees standing in a garden, but 9 
of them have been cut down. How many remain? 
Answer. 9 trees from 16 trees leave 7 trees. 


3. If you should buy 6 books, and pay 9 cents apiece 
for them, how many cents would the whole cost? 

Answer. If one book cost 9 cents; 6 books will 
cost 6 times 9 cents. 6 times 9 cents are 54 cents. 


4. If 5 plates he on one side of a table, and 4 on 
the other, how many are there on both sides? 


5. While a flock of 15 wild geese were flying over, 
a gunner shot 4 of them. How many escaped? 


6. A market-man sold 10 barrels of apples, at 3 dol- 
lars a barrel. How many dollars did he receive ? 


7. Alfred learned the answers of 13 questions, but 
he forgot 4 of them. How many did he remember ? 


8. How many cents will it take to buy two pic- 
tures, if one cost 3 cents, and the other 9 cents? 


9. Lucy has 6 picture-books, that cost 8 cents 
apiece. How many cents did the whole cost ? 


10. 'Phere are 17 apples in a fruit-hasket, but 8 of 
them are defective. How many are sound? 


li. Victoria has 4 sisters older than herself, and 3 
younger than herself. How many sisters has she ? 


46 MISCELLANEOUS EXAMPLES. 


Lesson Seconp. II. 


1. James has 28 cents, with which he is going to 
puy pencils, at 4 cents apiece. How many can he buy ? 

Answer. He can buy as many pencils as there are 
times 4 in 28. 4 in 28, 7 times. 

‘The expression in this answer may be varied thus} 
— He can buy as many pencils as 4 is contained 
times in 28. Or thus;— As many times as 4 is con- 
tained in 28, so many pencils he can buy. 


2. If it take 6 boys to play one game at ball, how 


many games can 30 boys play at the same time? 
3. Ifa kite cost 9 cents, and a whistle cost 7 cents, 


how many cents will it take to pay for both? 


4. A boy, who had 16 buttons on his jacket, lost 
off 5 of them. How many still remained on? 

5. How many oranges can you buy for 27 cents, 
when you can buy them for 3 cents apiece? 


6. If oranges are sold at the rate of 3 cents apiece, 
how many cents will it take to buy 8 oranges? 


7. A boat, that was crossing the river with 18 
boys in it, was upset by the wind, and 7 of the boy 
were drowned. How many of them were saved? 


» 8. I saw 8 ladies pass up street, and 4 others pass 
down street. How many passed both ways? 


9. Charles was kept away from school, by sick- 
ness, 42 days. How many weeks was he away? 


10. Jane and Edward went to a toy-shop together. 
Jane spent 6 cents, and Mdward spent 6 times as 
much. How many cents did Edward spend ? 


11. A boy, who had 16 cents, paid away 9 cents 
for a ball. How many cents had he remaining ? 


12. ‘The sun rises every day, and there are 7 days 
in a week, Uv many times does it rise in 7 weeks? 


13. Suppose that a man ean cut down 9 trees in a 
day, and that he can cut down 6 times as many ina 
week ;—— how many can he cut down in a week ? 


MISCELLANEOUS EXAMPLES. 47 


Lesson ‘T'uirp. ILI. 


1. There are 5 boys to pay 50 cents for breaking a 
square of glass. How much must each boy pay ? 

Answer. Each boy must pay as many cents as 
there are times 5 in 50. 5 in 50,10 times. ‘There- 
fore, each boy must pay 10 cents. 

2. A farmer, who raised 48 lambs, found that 1 
lamb in every 6 was black. How many were black ? 

3. In fishing this morning, I caught 13 fishes; but 
7 of them escaped. How many had I remaining ? 

4. There were 5 pears grew upon each of 3 young 
trees. How many pears were there in all? 

5. If you wished to divide 54 nuts equally among 
6 boys, how many would you give to each boy? 

6. If 8 girls recite, and each of them answer 4 
questions, how many questions will they all answer ? 

7. There are 12 squares of glass in a window, and 
only 7 of them are whole. How many are broken: 

8. If 8 barrels of flour can be carried on one cart, 
how many barrels can be carried on 6 carts? 

9. A little boy gave 40 kernels of corn to 5 ducks. 
How many kernels were there for each duck ? 


10. Martha is 12 years old, and Victoria is 5 years 
old. Now, what is the difference in their ages? | 


11. There are 6 rose-bushes on one side of a gar- 


den path, and 8 on the other. How many on both? 


12. If it take 8 squares of glass to make one 
window, how many are required for 8 windows ? 


13. A lady bought 6 yards of silk riband, and paid 
48 cents for it. How much was it a yard? 

14, Frances has 21 cents, with which she will buy 
cakes, at 3 cents apiece. How many can she buy? 

15. There were 4 huntsmen went out in a hunting 
party, and each huntsman had 9 greyhounds, How 
many greyhounds were there altogether ? 


48 MISCELLANEOUS EXAMPLES. 


Lesson FourtnHn. LY. 


1. If the price of one writing-book be 8 cents, how 
many cents must be paid for 4 writing-books ? 

2. If a baker use 18 barrels of flour in 9 weeks, 
how many barrels does he require for one week ? 

3. If there be 9 lines ruled across every page of a 
writing-book, how many lines are there on 5 pages? 

4. Charles had 17 cents; but he has paid out 6 
cents for a book. How many cents has he left ? 

5. Henry paid 10 cents for a knife, 8 for a pencil, 
and 4 for a box. How many cents did he spend ? 

6. How many yards of cloth can be bought for 27 
dollars, allowing the price to be 3 dollars a yard? 

7. 24 persons went across the river in 4 ferry-boats. 
What number were there to go in each boat? 

8. Suppose a goldsmith to make 5 finger-rings in 
one day ;——how many can he make in 9 days? 

9. If 49 dollars should be divided equally among 7 
sailors, how many dollars will each sailor receive ? 


10. There is now another Arithmetic for’ you, 
larger than this, called the SECOND PART. If you 
are twice as long in that book as you have been in 
this, in what time will you get through it? 


END OF PART FIRST. 


Note to Teachers. The SECOND PART of the North American 


Arithmetic is prepared especially to succeed the use of this little book. 


It contains a complete system of Mental and Written Arithmetic, sufficiently 
extensive for all the purposes of common business. No teacher need 
apprehend any difficulty in teaching from the Seconp Part, for the work 


is made perfectly plain and easy. Fractions, in particular, are rendered ° 
as simple as whole numbers. ‘The book may be obtained in the chief © 
- commercial place of every state, ces : 


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